The invention relates to a process for the cultivation of living cells in which the cells are cultivated on a support structure (14) and to the use of a structure comprising crystalline cellulose. The invention relates further to a process for the production of a support structure (14) of cellulose for the cultivation of living cells, comprising the steps:                preparation of a hollow mould;        cultivation of cellulose-forming organisms in an interior space formed by the hollow mould, in order to allow the support structure to grow in the interior space;        demoulding of the hollow mould; to a support structure (14) for the cultivation of living cells, to a support structure (14) for the cultivation of living cells, having at least one tubular void (15) which branches in at least one location, wherein at least some of the branches converge again in a different location, to a support structure (14) for the cultivation of living cells, having in its inside a plurality of voids which are separate from one another, and to a hollow mould for the preparation of a support structure (14) comprising crystalline cellulose for the cultivation of living cells.        